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<H1>Tutorial on Type Analysis</H1>
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<H1><A NAME="SEC4" HREF="typetutorial_toc.html#SEC4">Type Checking in Expressions</A></H1>
<P>
Expressions consist of typed names and literals and of operators
that are applied to operands of certain types and yield a result
of a certain type. Determining the types of expressions and 
checking the related type rules of the language is a significant
subtask of type analysis. The type rules of languages are usually
formulated in terms of concepts like "type of program constructs 
and entities", "signature of operators", "operator overloading", 
"type conversion". They have common and well-understood meaning
for type analysis in general. Of course, the type rules established 
for a particular language instantiate these concepts in a specific
way, e.g. define a specific set of operators with their signature
and state which conversions may be applied to resolve overloading.
<P>
Eli's type analysis module <CODE>Expression</CODE> provides reusable 
roles and computations to formulate the language specific 
instantiation of the concepts mentioned above. The type analysis
for expressions is generated from such a specification.
<P>
<I>Expression module</I>[20]==
<PRE>
$/Type/Expression.gnrc:inst
</PRE>
<PRE>
This macro is invoked in definition 26.
</PRE>
<P>
This module carries out type analysis on expression trees, 
which are subtrees made up of connected expression nodes. 
An expression node is a node representing a program construct
that yields a value of a certain type.
The module provides the role <CODE>ExpressionSymbol</CODE> to be inherited by
symbols that are expression symbols in that sense:
<P>
<I>Expression symbols</I>[21]==
<PRE>
SYMBOL Expression INHERITS ExpressionSymbol END;
SYMBOL Variable INHERITS ExpressionSymbol END;
</PRE>
<PRE>
This macro is invoked in definition 27.
</PRE>
<P>
The type of each expression node is characterized by two attributes: 
<CODE>ExpressionSymbol.Type</CODE> describes the type of the values this
expression may yield. <CODE>ExpressionSymbol.Required</CODE> may be used to
specify that the upper context requires the expression to yield 
a value of a particular type. As <CODE>ExpressionSymbol.Required</CODE> is
used to compute <CODE>ExpressionSymbol.Type</CODE>, it may not depend
on the <CODE>Type</CODE> attribute.
<P>
Expression symbols may occur in different contexts with respect to
the structure of the expression trees: root contexts, leaf contexts, and
inner contexts. The module provides different computational roles
for those contexts. In leaf contexts the type of the leaf expression
must be stated using the computational role <CODE>PrimaryContext</CODE>.
Note that in the third role below the expression node is a leaf
with respect to the expression tree, although the context has one
subtree, that is not an expression node:
<P>
<I>Leaf nodes</I>[22]==
<PRE>
RULE: Expression ::= IntNumber COMPUTE
  PrimaryContext (Expression, intType);
END;

RULE: Expression ::= 'true' COMPUTE
  PrimaryContext (Expression, boolType);
END;

RULE: Expression ::= 'false' COMPUTE
  PrimaryContext (Expression, boolType);
END;

RULE: Variable ::= UseIdent COMPUTE
  PrimaryContext (Variable, UseIdent.Type);
END;
</PRE>
<PRE>
This macro is invoked in definition 27.
</PRE>
<P>
The computational role <CODE>TransferContext</CODE> is used for contexts
that have an expression node on the left-hand side and one on the
right-hand side, and both have the same type properties:
<P>
<I>Transfer nodes</I>[23]==
<PRE>
RULE: Expression ::= Variable COMPUTE
  TransferContext (Expression, Variable);
END;
</PRE>
<PRE>
This macro is invoked in definition 27.
</PRE>
<P>
The node representing an assignment statement has two children.
Both are considered as roots of expression trees.
For the <CODE>Variable</CODE> the assignment context does not impose
any restriction on its type; hence, nothing is specified for
that node:
<P>
<I>Assignment</I>[24]==
<PRE>
RULE: Statement ::= Variable '=' Expression ';' COMPUTE
  RootContext (Variable.Type, , Expression);
  Indication (assignOpr);
END;
</PRE>
<PRE>
This macro is invoked in definition 27.
</PRE>
<P>
<CODE>explain the purpose of assignOpr??</CODE>
<P>
The <CODE>Expression</CODE> on the right-hand side of the assignment
is required to yield a value of the type of the <CODE>Variable</CODE>.
<P>
An expression in the role of a statement is another example for
a root context. On execution the value of the expression   will
just be discarded. Hence, there is no requirement on its type
to be stated or checked:
<I>Expression statement</I>[25]==
<PRE>
RULE: Statement ::=  Expression ';' END;
</PRE>
<PRE>
This macro is invoked in definition 27.
</PRE>
<P>
<B>Expression.specs</B>[26]==
<PRE>
<I>Expression module</I>[20]
</PRE>
<PRE>
This macro is attached to a product file.
</PRE>
<P>
<B>Expression.lido</B>[27]==
<PRE>
<I>Expression symbols</I>[21]
<I>Leaf nodes</I>[22]
<I>Transfer nodes</I>[23]
<I>Assignment</I>[24]
<I>Expression statement</I>[25]
</PRE>
<PRE>
This macro is attached to a product file.
</PRE>
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